Eur. Phys. J. E (2015) 38: 71
https://doi.org/10.1140/epje/i2015-15071-x

Regular Article

On the relevance of disorder in athermal amorphous materials under shear

¹ LIPHY, Univ. Grenoble Alpes, F-38000, Grenoble, France
² LIPHY, CNRS, F-38000, Grenoble, France

^* e-mail: Elisabeth.Agoritsas@ujf-grenoble.fr

Received: 19 January 2015
Revised: 12 May 2015
Accepted: 27 May 2015
Published online: 7 July 2015

Abstract

We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called Hébraud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems.